How to make a tetrahedron solid and grid?
This is fundamentally impossible because (surprisingly!) the platonic tetrahedron is not space-filling.
The dihedral angle of two adjacent faces of a regular tetrahedron is arccos(1/3) ≈ 70.53. So if you put 5 regular tetrahedrons together it makes 70.53*5=352.65 which is not quite the 360 you would need to fill space.